lean artifact · pending
Artifact ↗Source authenticated
The Carathéodory Conjecture on Umbilic Points
Only the smooth case falls. Hamburger's real-analytic theorem is untouched, and the counterexample is explicitly a object, so the conjecture's classical analytic form remains true. The gap between the two is the whole content of the result.
Exact FrontierDelta
disproved→disproved
Scope and record
Occurred: Oct 29, 2026
Delta type: REGISTRY REVISION
Assumptions: VibeMathed verification: lean-checked. Publication: announcement. AI contribution: ai-assisted. VibeMathed editorial classifications, scores, notes, relations, and dataset structure are CC BY 4.0. Source statements and linked content retain their own rights.
Canonical aliases: The $C^\infty$ Carathéodory Conjecture on Umbilic Points · Carathéodory conjecture (smooth)
Confidence: Not scored
Registry verification: lean checked · announcement · candidate
Attribution
VibeMathed
registry · event recorded by
Claude
model · ai model contributor · Anthropic
Codex
model · ai model contributor · OpenAI
Levent Alpöge
human · human collaborator
John-Paul Smith
human · human collaborator
Artifacts and verifiers
formal registration · pending
Artifact ↗Compute record
No linked compute attempts recorded.
Lineage and corrections
Corrects The Carathéodory Conjecture on Umbilic Points →
Supersedes The Carathéodory Conjecture on Umbilic Points →
VibeMathed record: The Carathéodory Conjecture on Umbilic Points evidence for this event
Ghomi, Open Problems in Geometry of Curves and Surfaces (Problem 8.1) evidence for this event
The Carathéodory Conjecture on Umbilic Points evidence for this event
This event attributed to Claude
This event attributed to Codex
Only the smooth case falls. Hamburger's real-analytic theorem is untouched, and the counterexample is explicitly a object, so the conjecture's classical analytic form remains true. The gap between the two is the whole content of the result. parent of this event
The Carathéodory Conjecture on Umbilic Points parent of this event
Lean proof, sorry-free at the pinned commit evidence for this event
The informal proof accompanying the formalization evidence for this event
Lean statement of the smooth and analytic conjectures evidence for this event
This event attributed to John-Paul Smith
This event attributed to Levent Alpöge
Act on this frontier